2.3 Proving Theorems Midpoint & Angle Bisector Theorem

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Presentation transcript:

2.3 Proving Theorems Midpoint & Angle Bisector Theorem PROOFS ARE FUN! PROOFS ARE FUN! I’m not going to lie, it’s time to justify! Mr. Watanabe Honors Geometry

What is the definition of a midpoint What is the definition of a midpoint? If M is the midpoint of segment AB, then AM=MB What is the definition of an angle bisector? If ray BX is the angle bisector of angle ABC , then m<ABX = m<XBC.

What is a theorem? What is deductive reasoning? A theorem is a statement that can be proved by using information that is known to be true. The purpose of this lesson is to begin the topic of what a proof is and how theorems are proved. Deductive Reasoning- 2 column proofs are classic examples! We have proved statements by reasoning from postulates, definitions, theorems, and given information.

MIDPOINT THEOREM

ANGLE BISECTOR THEOREM

WHAT ARE REASONS USED IN PROOFS? GIVEN INFORMATION DEFINITIONS POSTULATES (These include properties from algebra) THEOREMS (Must be proven first)

Let’s tackle some proofs!!! Segment Addition Postulate Angle Addition Postulate Definition of midpoint Definition of angle bisector Definition of congruency Algebra Properties of Equality (+, -, X, / ) Reflexive , Symmetric, Transitive (Equality & Congruency) Substitution